 95468 Delshams A., RamirezRos R.
 PoincareMelnikovArnold Method for Analytic Planar Maps
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Oct 26, 95

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Abstract. The PoincareMelnikovArnold method for planar maps
gives rise to a Melnikov function defined
by an infinite and (a priori) analytically uncomputable sum.
Under an assumption of meromorphicity, residues theory can be applied
to provide an equivalent finite sum.
Moreover, the Melnikov function turns out to be an elliptic function and
a general criterion about nonintegrability is provided.
Several examples are presented with explicit
estimates of the splitting angle.
In particular, the nonintegrability of nontrivial symmetric
entire perturbations of elliptic billiards is proved,
as well as the nonintegrability of standardlike maps.
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